Question: Factor completely. $49p^8+42p^4+9=$
$\begin{aligned} &\phantom{=}49 p ^8 + 42 p ^4 + 9 \\\\ &= ({7 p ^4})^2 + 2({7 p ^4})({3 })+({3 })^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({7 p ^4})^2 + 2({7 p ^4})({3 })+({3 })^2 \\\\ &=({7 p ^4} + {3 })^2 \end{aligned}$ In conclusion, $49 p ^8 + 42 p ^4 + 9 =(7 p ^4 + 3 )^2$ Remember that you can always check your factorization by expanding it.